Dynamics of virus infection model with nonlytic immune response induced by stochastic noise

In this paper, we study the effect of stochastic noise on the virus infection model with nonlytic immune response. Firstly, the mathematical model describing the virus infection with nonlytic immune response is presented. The basic reproduction number is derived and the stability of disease-free state E0 and disease state E1 are analysed. Then the threshold conditions for extinction and persistence of the virus are derived by the rigorous theoretical proofs. It is found that when the noise is large enough, the virus will die out without constraint. When the noise is small, the virus will become extinct under the condition R0*<1 and persistence under R0**>1. Besides, the upper bound and lower bound for persistence have been given. At last, some numerical simulations are carried out to support our results. The conclusion of this paper could help provide the theoretical basis for the further study of the virus infection.